Combining previously unconnected computational methods, this monograph discusses the latest basic schemes and algorithms for the solution of fluid, heat and mass transfer problems coupled with electrodynamics. It presents the necessary mathematical background of computational thermo-fluid dynamics, the numerical implementation and the application to real-world problems. Particular emphasis is placed throughout on the use of electromagnetic fields to control the heat, mass and fluid flows in melts and on phase change phenomena during the solidification of pure materials and binary alloys. However, the book provides much more than formalisms and algorithms; it also stresses the importance of good, feasible and workable models to understand complex systems, and develops these in detail.
Bringing computational fluid dynamics, thermodynamics and electrodynamics together, this is a useful source for materials scientists, PhD students, solid state physicists, process engineers and mechanical engineers, as well as lecturers in mechanical engineering.

INTRODUCTION
Heat and Fluid Flows in Material Science and Engineering
Overview of the Present Work
MATHEMATICAL DESCRIPTION OF PHYSICAL PHENOMENA IN THERMOFLUIDDYNAMICS
Conservation Equations for Continuum Media
Boundary and Initial Conditions
Conservation Equations in Electromagnetics
DISCRETIZATION APPROACHES AND NUMERICAL METHODS
The Finite Difference Method
The Finite Volume Method
Solution of Linear Equation Systems
CALCULATIONS OF FLOWS WITH HEAT AND MASS TRANSFER
Solution of Incompressible Navier-Stokes Equations
Pressure and Velocity Coupling: SIMPLE Family
Illustrations of Schemes for Flow with Heat Transfer
Complex Geometry Problems on Fixed Cartesian Grids
CONVECTION-DIFFUSION PHASE CHANGE PROBLEMS
Some Aspects of Solidification Thermodynamics
Modeling of Macroscale Phase Change Phenomena
Turbulent Solidification
Microscale Phase Change Phenomena
Crystal Growth Modelling
Melting of Pure Gallium under the Influence of Natural Convection
APPLICATION I: SPIN-UP OF A LIQUID METAL IN CYLINDRICAL CAVITIES
Spin-Up of Isothermal Flow Driven by Rotating Magnetic Field
The Impact of the Buoyancy Force on the Spin-Up Dynamics
APPLICATION II: LAMINAR AND TURBULENT FLOWS DRIVEN BY A RMF
Laminar Flows: State of the Art
Turbulent Flows
APPLICATION III: CONTACTLESS MIXING OF LIQUID METALS
Mixing under Zero Gravity Condition
The Impact of Gravity on the Mixing
APPLICATION IV: ELECTROMAGNETIC CONTROL OF BINARY METAL ALLOYS SOLIDIFICATION
Control of a binary metal alloy Solidification by use of AC fields
Control of Solidification by use of Steady Electromagnetic Fields
The Impact of a Steady Electrical Current on the Unidirectional Solidification
The Impact of an Electric Field on the Shape of a Dendrite
The Impact of Parallel Applied Electric and Magnetic Fields on Dendritic Growth

Petr Nikrityuk is head of the research group "Interphase Phenomena" within the "Virtual High Temperature Conversion Processes" (VIRTUHCON) project at the Technical University Freiberg, Germany. He studied mechanical engineering at the Moscow Aviation Institute where he also obtained his PhD on the topic of mathematical modeling of thermal processes. Before taking up his current position in Freiberg, Petr Nikrityuk worked as software developer in the field of computational fluid dynamics and as a research scientist in the Institute for Aerospace Engineering at the Technical University Dresden, Germany.

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